On directed incomplete transversal designs with block size five (Q2713651)

Consider the definition of a transversal design \(\text{TD}(k,v)\) and replace blocks by ordered \(k\)-tuples. This yields a definition of a directed transversal design \(\text{DTD}(k,v)\). Similarly, define holey designs \(\text{DTD}(k,v)-\text{DTD}(k,u)\) as analogs of \(\text{TD}(k,v)-\text{TD}(k,u)\). It is clear that by replacing a block by two ordered \(k\)-tuples one can change a transversal design to a directed one. The paper utilizes this fact and an earlier classfication of TD\((5,v)-\text{TD}(5,u)\) to show (after solving a number of specific cases) that \(\text{DTD}(5,v)-\text{DTD}(5,u)\) exists if and only if \(v \geq 4u\).